Free Access
Issue
ESAIM: M2AN
Volume 42, Number 4, July-August 2008
Page(s) 683 - 698
DOI https://doi.org/10.1051/m2an:2008019
Published online 05 June 2008
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  2. R. Abgrall and S. Karni, A relaxation scheme for the two-layer shallow water system, in Proceedings of the 11th International Conference on Hyperbolic Problems (Lyon, 2006), Hyperbolic problems: theory, numerics, applications, S. Benzoni-Gavage and D. Serre Eds., Springer (2007) 135–144.
  3. E. Audusse and M.-O. Bristeau, A well-balanced positivity preserving “second-order” scheme for shallow water flows on unstructured meshes. J. Comput. Phys. 206 (2005) 311–333. [CrossRef] [MathSciNet]
  4. E. Audusse, M.-O. Bristeau and B. Perthame, Kinetic schemes for Saint-Venant equations with source terms on unstructured grids. INRIA Report, RR-3989 (2000).
  5. E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050–2065 (electronic). [CrossRef] [MathSciNet]
  6. D.S. Bale, R.J. Leveque, S. Mitran and J.A. Rossmanith, A wave propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput. 24 (2002) 955–978 (electronic) [CrossRef] [MathSciNet]
  7. M. Baudin, C. Berthon, F. Coquel, R. Masson and Q.H. Tran, A relaxation method for two-phase flow models with hydrodynamic closure law. Numer. Math. 99 (2005) 411–440. [CrossRef] [MathSciNet]
  8. C. Berthon and F. Coquel, Travelling wave solutions of a convective diffusive system with first and second order terms in nonconservation form, in Hyperbolic problems: theory, numerics, applications, Vol. I (Zürich, 1998), Internat. Ser. Numer. Math. 129, Birkhäuser, Basel (1999) 74–54.
  9. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004).
  10. F. Bouchut, S. Medvedev, G. Reznik, A. Stegner and V. Zeitlin, Nonlinear dynamics of rotating shallow water: methods and advances, Edited Series on Advances in Nonlinear Science and Complexity. Elsevier (2007).
  11. M. Castro, J. Macías and C. Parés, A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. ESAIM: M2AN 35 (2001) 107–127. [CrossRef] [EDP Sciences]
  12. Q. Jiang and R.B. Smith, Ideal shocks in a 2-layer flow. II: Under a passive layer. Tellus 53A (2001) 146–167.
  13. J.B. Klemp, R. Rotunno and W.C. Skamarock, On the propagation of internal bores. J. Fluid Mech. 331 (1997) 81–106. [CrossRef]
  14. M. Li and P.F. Cummins, A note on hydraulic theory of internal bores. Dyn. Atm. Oceans 28 (1998) 1–7. [CrossRef]
  15. C. Parés and M. Castro, On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. ESAIM: M2AN 38 (2004) 821–852. [CrossRef] [EDP Sciences]
  16. M. Pelanti, F. Bouchut, A. Mangeney and J.-P. Vilotte, Numerical modeling of two-phase gravitational granular flows with bottom topography, in Proc. of HYP06, Lyon, France (2007).
  17. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 (2001) 201–231. [CrossRef] [MathSciNet]
  18. J.B. Schijf and J.C. Schonfeld, Theoretical considerations on the motion of salt and fresh water, in Proc. of the Minn. Int. Hydraulics Conv., Joint meeting IAHR and Hyd. Div. ASCE (1953) 321–333.

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